Formula Explorer

Beam Deflection Calculator with Formulas

Review the core closed-form beam equations behind the standard one-span cases and compare the resulting deflection, moment, shear, and reactions with live inputs.

Formula Cases

Current Inputs

Span L (m)Elastic modulus E (GPa)Second moment of area I (cm^4)Uniform load w (kN/m)

Response Summary

Governing equation	delta_max = 5 w L^4 / (384 E I)
Maximum deflection	4.73 mm
Maximum moment	22.50 kN*m
Maximum shear	15.00 kN
Left reaction	15.00 kN
Right reaction	15.00 kN

Formula Steps

Maximum deflection

General form

delta_max = 5 w L^4 / (384 E I)

With current values

delta_max = 5 * 5.00 * 6.00^4 / (384 * 210 * 8,500)

Result

delta_max = 4.73 mm

Maximum moment

General form

M_max = w L^2 / 8

With current values

M_max = 5.00 * 6.00^2 / 8

Result

M_max = 22.50 kN*m

Maximum shear

General form

V_max = w L / 2

With current values

V_max = 5.00 * 6.00 / 2

Result

V_max = 15.00 kN

Case Assumptions

The uniform load is constant over the whole span.
Both supports provide vertical restraint only.
The beam uses constant stiffness along its length.